Solid Oxide Fuel Cells (SOFC) power plant systems have operational constraints on state variables, such as fuel cell temperature and pressure. In this research, a dynamic model of a SOFC power plant was derived and its accuracy was evaluated by using experimental plant data. The optimal operations to minimize start-up and shutdown time under various operational restrictions were also derived. Data on the start-up and shutdown of a real plant were used to evaluate the modeling accuracy. The results show that the modeling errors of SOFC inlet temperatures could be kept within 5.0% of the sensor ranges by including the heat-leak and the heat-pass of the apparatus in the model. The optimization results for start-up time and shutdown time showed that they could be reduced to 28% and 67% of the conventional operation times, respectively. Furthermore, the optimal operation to minimize energy consumption was derived for the periodic operation mode of weekly start-stop.